Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
Updated
Claim. The implication of Problem 1167, in the site's wording with no condition on or on the , is false. Take and . With a single color, the premise asks only for a subset of of size , which exists since . The conclusion asks for a subset of of size , which does not exist. Zeraoulia's note, A note on Erdős-Hajnal-Rado Problem #1167: a counterexample to the literal statement and remarks on the intended formulation, self-published on ResearchGate under the DOI linked above, gives this counterexample and discusses the conditions under which the question is meant.
Covers. The site's wording only; the corrected Statement of the problem page is not touched. That Statement adds the conditions , and of the Erdős–Hajnal list, and it is open.
Depends on. No page of this wiki.
Why it is rejected. It answers the site's wording, not the corrected Statement. Problem 1167 judges its corrected Statement, which adds the conditions and ; the problem page's Notes give the evidence for that reading. The counterexample has , so it settles no instance of the corrected Statement. The problem page's Notes credit the result.
Independent check. The
formal-conjectures statement file
for the problem proves the same counterexample (,
, ) as its test lemma
erdos_1167.unrestricted_is_false. That file is a statement file, not a
formalization of this note, and the corpus has not built it, so it gives no
formalized evidence.
Acceptance. None documented. The note has no journal record. The site labels the problem OPEN, and its curator's reply in the discussion thread points to the conditions of Komjáth's Problem 2 rather than accepting a disproof, so the reply is not acceptance. The claim is rejected, and acceptance would not change that, since the rejection concerns what the result answers.